Deep Holes and MDS Extensions of Reed–Solomon Codes
| Autor: | Krishna Kaipa |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Block code
Burst error-correcting code Berlekamp–Welch algorithm List decoding Reed–Muller code 020206 networking & telecommunications Data_CODINGANDINFORMATIONTHEORY 0102 computer and information sciences 02 engineering and technology Library and Information Sciences 01 natural sciences Computer Science Applications Combinatorics 010201 computation theory & mathematics Reed–Solomon error correction 0202 electrical engineering electronic engineering information engineering Tornado code Hardware_ARITHMETICANDLOGICSTRUCTURES Folded Reed–Solomon code Computer Science::Information Theory Information Systems Mathematics |
| Zdroj: | IEEE Transactions on Information Theory. 63:4940-4948 |
| ISSN: | 1557-9654 0018-9448 |
| DOI: | 10.1109/tit.2017.2706677 |
| Popis: | We study the problem of classifying deep holes of Reed–Solomon codes. We show that this problem is equivalent to the problem of classifying maximum distance separable (MDS) extensions of Reed–Solomon codes by one digit. This equivalence allows us to improve recent results on the former problem. In particular, we classify deep holes of Reed–Solomon codes of dimension greater than half the alphabet size. We also give a complete classification of deep holes of Reed–Solomon codes with redundancy three in all dimensions. |
| Databáze: | OpenAIRE |
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